Constraints on parity violating conformal field theories in d=3

We derive constraints on three-point functions involving the stress tensor, T, and a conserved U(1) current, j, in 2+1 dimensional conformal field theories that violate parity, using conformal collider bounds introduced by Hofman and Maldacena. Conformal invariance allows parity-odd tensor-structures for the < TTT > and < jjT > correlation functions which are unique to three space-time dimensions. Let the parameters which determine the < TTT > correlation function be t(4) and alpha(T), where alpha(T) is the parity-violating contribution. Similarly let the parameters which determine < jjT > correlation function be a(2), and alpha(J), where alpha(J) is the parity-violating contribution. We show that the parameters (t(4); alpha(T)) and (a(2); alpha(J)) are bounded to lie inside a disc at the origin of the t(4)-alpha(T) plane and the a(2) - alpha(J) plane respectively. We then show that large N Chern-Simons theories coupled to a fundamental fermion/boson lie on the circle which bounds these discs. The 't Hooft coupling determines the location of these theories on the boundary circles.